I appreciate if you could help me to find a reference (and a proof).
Combining Dirichlet theorem on primes in arithmetic progression with Chebotarev densitiy theorem, we know that given two positive ...

Below is the definition of a prime-partitionable integer taken from W. Holsztynski, R. F. E. Strube, Paths and circuits in finite groups, Discr. Math. 22 (1987) 263-272 and is apparently the same in ...

I am currently working on problem that I think could be expressed as an integer lattice problem.
Given $u \in \mathbb{R}^n$ and a bounded integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$ I would like ...

Let $\lambda$ be a self-dual Hecke character over a CM field $K$ with root number $-1$. How to show the existence of a finite order anticyclotomic Hecke character $\chi$ over $K$ such that the twist ...

If $A$ is a mixed characteristic complete DVR (I'm only actually interested in $\mathbf{Z}_p$) and $G/A$ is a closed subgroup scheme of $GL(n)$ whose generic fibre is connected reductive and split, is ...

A quick look at the primes in $\mathbb{Z}[i]$ suggests they might be evenly distributed by angle if we zoom out on a coarse enough scale.
I would like ask about the much weaker statement forgetting ...

Let $\widehat{F_2}$ be the pro-$\ell$ completion of the free group of rank 2, where $\ell$ is some prime.
Every outer automorphism of $F_2$ induces an outer automorphism of $\widehat{F_2}$, hence an ...

I have recently managed to show a sequence of sufficiency sets for the Collatz conjecture whose natural density approaches 0 (the set theoretic limit approaches the set $\{1\}$). It is an extension of ...

Suppose $f$ and $g$ are polynomials with integral coefficients and $f(\mathbb Z)\subset g(\mathbb Z)$. Is there any relation between $f$ and $g$?
For instance, this happens if $f=g\circ h$ for some ...

Suppose that $\Lambda_1, \Lambda_2$ are two sub-lattices of $\mathbb{Z}^n$ of full rank, defined by congruence modulo a prime $p$. That is, there exist two vectors with integer entries $\mathbf{a}, ...

Assume Goldbach's conjecture. Then for all integer $n$ greater than 1, there exists a non negative integer $r$ such that both $n+r$ and $n-r$ are prime. I call such an $r$ a primality radius of $n$, ...

Let $k$ be an algebraically closed field and $k_0$ a sub-field. Let $X,Y$ be two projective varieties defined over $k_0$. Suppose that that there exists a dominant morphism $f$ between $X_k=X\otimes ...

For someone who does not have a very extensive knowledge of number theory, what is a good intuitive explanation as to why there are only finitely many $\overline{\mathbb{Q}}$ isomorphism classes of ...

For the problem I am working on I have realised that some of the proofs could be slightly simplified if a certain number theoretic question has a positive solution. Now, the problem is in finite group ...

It is known that all smooth projective quartic hypersurfaces of suitably large dimension are unirational over $\overline{\mathbb{Q}}$. Are there any results regarding unirationality over $\mathbb{Q}$ ...